Question

A toy is in the from of a cone mounted on a hemisphere. The diameter of the base and the height
of the cone are 6cm and 4cm respectively determine the surface area of the toy.​

Answer 1

Answer:

$\frac{726}{7} cm^{2}$

Step-by-step explanation:

Here, the surface area of the cone will be lateral surface area because its will be not present here,

Similarly, here the area of the hemisphere will be lateral surface area.

The surface area of the toy will be the sum of the lateral surface are of cone and hemisphere.

So, lateral surface area of the cone =   πrl

We have given,

                         r = 6/2 = 3cm;

and                   h = 4cm;

now                   l =$\sqrt{r^{2} +h^{2} }$

                         l = $\sqrt{3^{2} +4^{2} }$

                         l = $\sqrt{9 + 16 }$

                         l = $\sqrt{25 }$ = 5cm

the surface area of cone = 22/7 * 5 * 3 = $\frac{330}{7}$$cm^{2}$

Now the surface area of hemisphere = 2π$r^{2}$

                                                = 2 * 22/7 * 3* 3

                                               = 18 * 22/7

                                                 = $\frac{396}{7}$$cm^{2}$

Now, adding both the areas;

                           = 330/7 + 396/7

                           =$\frac{726}{7} cm^{2}$

So, the area of the toy will be $\frac{726}{7} cm^{2}$.

That's all.

Answer 2

$\huge\underline\mathrm{GIVEN:-}$

• A toy is in the from of a cone mounted on a hemisphere
• The diameter of the base of the cone is 6 cm
• The height of the cone is 4 cm

$\huge\underline\mathrm{TO\:FIND:-}$

Find the T.S.A. of the toy = ?

$\huge\underline\mathrm{SOLUTION:-}$

We have given the diameter of the base and the height

of the cone are 6cm and 4cm respectively

Now, we have to find the radius

$\bf{Radius =}$ $\large{\bf {\frac{Diameter}{2}}}$

$\bf{Radius =}$ $\large{\bf {\frac{6}{2}}}$ = $\bf{3 \:cm}$

$\bf{Radius =}$$\bf{3 \:cm}$

$\large{\boxed{\bf{T.S.A.\: of \:toy = C.S.A.\: of \:cone \: + \: C.S.A. \:of\: hemisphere}}}$

T.S.A. of toy = πrl + 2πr²

To find the C.S.A. of cone, we need to find slant height (l) of the cone

$\implies$$\bf{l = }$$\bf\sqrt{{h}^{2} +{r}^{2}}$

$\implies$$\bf{l =}$ $\bf\sqrt{{(4)}^{2 }+{(3)}^{2}}$

$\implies$ $\bf{l =}$ $\bf\sqrt{16+9}$

$\implies$ $\bf{l =}$ $\bf\sqrt{25}$

$\implies$ $\large\bf{l = 5 cm }$

The slant height(l) of the cone is 5 cm

T.S.A. of toy = πrl + 2πr²

$\implies$ πr(l + 2r)....[since, the cone and hemisphere are on same base, there, radius of the base are same)

Putting the given values in formula

$\implies$ $\large{\bf {\frac{22}{7}}}$$\times$ 3(5 + 2$\times$3)

$\implies$ $\large{\bf {\frac{22}{7}}}$$\times$ 3(5 + 6)

$\implies$ $\large{\bf {\frac{22}{7}}}$$\times$ 3$\times$ 11

$\implies$ $\large{\bf {\frac{66\times11}{7}}}$

$\implies$ $\large{\bf {\frac{726}{7}}}$

$\implies$ 103.71 cm²

$\implies$ T.S.A. of cone = approx. 103.71 cm²